The Wacky World of Perovskites

David J. Singh

Oak Ridge National Laboratory

The mineral perovskite:

CaTiO3

“A minor ore of Ti”

Image from www.mindat.org: (mineral from Chelyabinsk, Russia)

Supported by DOE, BES, Materials Sciences and Engineering and the S3TEC EFRC.

WARNING

If you do not ask questions, I will.

(corollary) If you do not contradict me, I

will.

Structure of CaTiO3

O

Ca

Ti Key structural feature

is corner sharing TiO6

octahedra.

CaTiO3 is pseudocubic

(orthorhombic, a

distortion of a cubic

structure).

Perovskite Variants

Layered Perovskites

6

Cubic Perovskite

Double Perovskite, e.g. Sr2YRuO6

What’s Interesting

• Tendency towards sometimes complex structure distortions (as

in e.g. CaTiO3.

• Many perovskites are metallic and many are not. Sometimes

one can tune between metallic and insulating states by “small”

perturbations.

• Many perovskites exist with magnetic ions both on the Ca site,

such as various rare earth’s and the B-site, such as various 3d

transition elements e.g. GdFeO3.

• There is often strong coupling between degrees of freedom in

perovskites – structure – magnetism – electronic properties.

• The perovskite family allows wide chemical flexibility – many

compounds can be formed.

Example: CMR Manganites

Ramirez et al. (1996) Schiffer et al. (1995)

La1-xCaxMnO3 Phase Diagram

All phases show local moment

magnetism as expected for 3d

high spin ion due to Hund’s

coupling.

Wide variety of magnetic

phases: coupled metal insulator

transitions, orbital orderings,

spin orderings.

Properties

• Main families of ferroelectrics used in applications –

Pb(Zr,Ti)O3, BaTiO3, (K,Na)NbO3, (Ba,Sr)TiO3 etc.

• Electronics, medical ultrasound, actuators, sonars,

microwave devices, motion detectors …

• Colossal magnetoresistance (manganites).

• High TC half-metal ferromagnets: Sr2MoFeO6 …

• High-Tc superconductors: Cuprates, (Ba,K)BiO3.

• ….

STRUCTURE AND IONIC SIZE

(Ferroelectrics)

SSN21 Seawolf

What are Ferroelectrics?

+Vf

0

Q

Note analogy with Ferromagnets

Producing a Ferroelectric

- + - + - + Linear chain of charged

atoms (e.g. H and F)

- + - + - +

- + - + - + Tensile strain

Symmetry

breaking

Coulomb interactions and covalent bonds favor ferroelectric

Closed shell repulsion oppose ferroelectric

or

- + - + - +

Medical Imaging

PZT

2000 Piezocrystal:

2004

Materials discovery to commercial products in less than seven

years

Electronics and Others

Ferroelectric memories:

Ramtron

Fujitsu

Samsung

Passive components:

EPCOS and many others

Microwave/Radar:

Phased array radar lens

J.B.L. Rao et al.

Piezoelectric fuel injector (Bosch)

Actuators:

Pyroelectric Effect

Motion detectors,

X-ray generators

Neutron generators

How Does PZT Work?

Cubic Perovskite Structure

TO() unstable

phonon

(Ferroelectric)

Tetragonal FE

Ground state can be tetragonal,

orthorhombic, rhombohedral or monoclinic.

Jaffe, Cook, and Jaffe, (1971).

Piezoelectric Ceramics

PZT near the

morphotropic

phase boundary

is the basis of

current devices

What is the Size of an Atom?

The Size of an Atom

d

Inter-atomic distance,

d = rA + rB

Crystallographic data

“defines” the “sizes” of

atoms.

• Goldschmidt; Pauling; Shannon and Prewitt

INSTABILITIES OF PEROVSKITES

PbTiO3

Chemical Understanding:

• Main interactions are (1) Coulomb (ionic) and (2) Closed shell

repulsions. Competition of bond lengths

drives most perovskite

instabilities.

Tolerance Factor:

t = (rA+rO)/2(rB+rO)

(a) t>1 (B ion [Ti] is too small)

B site off-centering and

ferroelectricity (BaTiO3, KNbO3)

(b) t<1 (A ion [Pb] is too small)

Rotation of octahedra, e.g.

CaTiO3, GdFeO3, LaMnO3… (the

great majority of perovskites).

Role of Pb on the Perovskite A-Site

• Pb allows t<1 perovskites to be ferroelectric instead of

Pnma or similar.

Electronic Structure:

Pb O Zr/Ti

6s

6p

2p

3d/4d

EF

Cross-gap hybridization:

• Increases Z*

• Softens interactions

• Increases polarizability

• Favors Ferroelectricity

R.E. Cohen, 1992

What’s going on here?

EF

unoccupied

occupied

H

E

Occupied states decrease in energy a chemical bond

n.b. mixing of occupied states is not a bond!

Are there Pb-free materials

that are as good as or

even better than the Pb-

based materials, e.g. PZT?

Answer was long thought to

be no…

… but results in the last

decade for materials such as

BiFeO3 suggest a closer

look.

BiFeO3:

• A very high polarization material

based on structure

(Tomashpol’skii, 1967), but not

usable due to conductivity.

Lebeugle et al., APL 2007, room temp.

How Much of a Good Thing is Enough?

from www.crystalmaker.co.uk

The Perovskite Structure

Pauling Rules - JACS 51, 1010 (1929).

1. “the cation-anion distance being

determined by the radius sum and

the coordination number of the

cation by the radius ratio”

2. “charge of each anion tends to

compensate the strength of the

electrostatic valence bonds reaching

it”

3. “shared edges and particularly

shared faces … decreases stability;

this effect is large for cations with

large valence …”

Problem:

• Bi3+ vs. Pb2+ implies lower average B-site charge.

• Bi3+ has c.r.~1.3 Å << Pb2+ (1.63 Å).

Bi perovskites are often difficult to make.

INSTABILITIES OF PEROVSKITES

Single sub-lattice off-centering (LDA):

Expt. Volume: 6% Expansion:

INSTABILITIES OF PEROVSKITES Classification:

1. UA : Unstable against A-site off-centering (PZ).

• t<1

• also unstable against rotation.

2. UB: Unstable against B-site off-centering (BT).

• t>1

3. UAB: Unstable against both A- and B-site off-centering (PT).

• t~1

• Instability not driven by tolerance factor.

4. S: Stable against sub-lattice off-centering (BZ), t~1, or

ferroelectrics like KTN.

PZT is an alloy between UA and UAB end-points.

Not understood by tolerance factor alone.

INSTABILITIES OF PEROVSKITES

LDA calculations constrained to rhombohedral ferroelectric

Displacements in Bohr along x direction (0.529 3 Ang. disp.)

Ghita, Fornari, Singh, Halilov (‘05)

Cooperative A-site and B-site displacements

characterize good perovskite ferroelectrics

Phonons In Ferroelectric Perovskites

First Principles Calculations

of Ghosez et al. (1999):

• note R point instabilities in

PZ and PT but not BT.

• Note different coherence

lengths for zone center

and zone boundary

instabilities.

ROTATIONAL (TILT) MODES

• Distortion around A

(A-O bond lengths)

• Bends B-O-B bonds

but only bond

lengths in second

order. (n.b. breathing

mode is usually stiff).

• Driven by pressure

and/or tolerance

factor if octahedra

are stiff.

• Alternate is A-site

off-centering (Pb).

Volume Dependence of Modes (50-50 PZT)

Ferroelectric Mode () Rotational Mode (R)

•Fornari and Singh, 2000.

• Volume dependence of FE and Rotational Instabilities is large and opposite.

• Implies co-existence in disordered alloys due to local stress fields.

•Confirmed, Ranjan et al, PRB 2002 (neutron scattering).

What If …

… we could eliminate the tilt instability from

arbitrary t<1 perovskites?

First principles get ferroelectricity

Strain Coupling Allowing only ferroelectric states & at the LDA lattice parameter:

• Note rhombohedral ferroelectric phase is

very much more stable than tetragonal.

• Note large ferroelectric energy.

• Also note the large c/a of the tetragonal.

t ~ 0.9

Why are these

so different

R-FE vs. T-FE LDA ENERGETICS

•A site ion is 12-fold coordinated (very isotropic).

•B site ion is 6-fold (octahedral). Expectation:

Without strain A-site

driven materials (t<1)

should be isotropic. With

strain they should all be

tetragonal.

B-site driven materials

(t>1) should be

rhombohedral unless

strain is very important.

Not true: Reason is

cooperativity involving B-

site.

Concept of Bond Valence

• I.D. Brown based on crystallography (c.f. ionic radius).

• For a given valence a sum involving bond lengths is nearly

constant A sum involving bond lengths yields valence.

Tables of R0 and b are in various sources:

Brown, I. D.; The Chemical Bond in Inorganic Chemistry - The Bond Valence Model.

IUCr monographs on Crystallography 12, Oxford University Press, (2002).

Brown, I. D.; in Structure and Bonding in Crystals, edited by M. O'Keeffe & A.

Navrotsky, Vol. II, pp. 1-30. New York; Academic Press (1981).

Some Consequences of Bond Valence

Focusing on metal site:

Push an O in and the others go out.

Focusing on O sites:

Mechanism for interplay of A and B site

displacements and local correlations of

cation displacements.

Application to Ferroelectrics

•Grinberg, Cooper, Rappe, Nature (2002).

•Structure relaxation of large supercells of PZT.

Complex structures with non-collinear cation displacements could

be understood in terms of bond valence. Potential model based

on this was made and used to study very large cells – PDF’s

agree with experiment.

Pb displacements

avoid Zr rich

directions.

CRYSTAL FIELD AND

JAHN-TELLER DISTORTIONS

From Vinobalan Durairaj web site

The d Orbitals

eg orbitals point at the

corners of the octahedron

t2g orbitals do not.

From wikipedia

The O p Orbitals

• One of these (p) points at the center of the octahedron.

• The other two (p) are perpendicular.

The Octahedral Crystal Field

E

O p

M d

H

M t2g

M e2g

O p

O p

In transition metal oxides crystal field is due (mostly)

to hybridization

bonding

anti-bonding

bonding

anti-bonding

An Example: PbZrO3 (cubic)

Note Zr d contribution

at bottom of O bands

Jahn-Teller Effect

E

M eg EF

For a sufficiently narrow level with partial occupation,

we expect a splitting to lower the energy. How does

this happen (i.e. what is H)?

Large band-width works against this.

eg*

eg E

H

Jahn-Teller Effect z

d z2

d x2-y2

A kind of orbital ordering.

The same thing works for t2g orbitals

but the effect is (much) smaller

because these are involved in weak

bonds instead of strong bonds

Cooperativity

Jahn-Teller is long range – corresponding zone boundary modes have long

coherence length (zone center also possible – ferroelastic)

BAND FORMATION (eg and t2g)

Geometric Considerations (O and B-site)

Cubic structure:

• O – O distance is a/2 (can

have direct hopping)

• B – B distance is a (too far for

much direct hopping).

Metal bands are formed via

hopping through O.

1D linear chains along Cartesian

directions 1D and 2D

bands.

Geometric Considerations (O and B-site)

Cubic SrRuO3

Flat bands

Planar Fermi surfaces

(e.g. cubes rather than

spheres).

M. Opel

High-Tc Electronic Structures are 2D

Pickett, Cohen, Krakauer, Singh

Hopping Through O O px,py,pz point along Cartesian directions (90 degrees apart):

Cubic: Tilted:

• Maximum pd hopping.

• Wide eg bands.

• Reduced pd hopping.

• Narrower eg bands.

• Additional splittings due to

symmetry lowering.

• Can broaden t2g bands

depending on details.

• Direct m-m hopping.

Tilts reduce band width but

do not reduce hybridization

(i.e. crystal field).

Tilts and Hopping Through O

(Friedt et al., 2000)

(Sr,Ca)2RuO4 (Nakatsuji)

MAGNETISM: Moment Formation

Local Atomic Moments (Hund’s Rules)

1. For a given electron configuration, the term with maximum

multiplicity (maximum S) has the lowest energy (exchange /

Coulomb correlation).

2. For a given multiplicity, the term with the largest value of L has the

lowest energy (Coulomb correlation).

3. For a given term, in an atom with outermost sub-shell half-filled or

less, the level with the lowest value of J lies lowest in energy. If the

outermost shell is more than half-filled, the level with highest value

of J is lowest in energy (spin-orbit).

1st Rule:

In solids levels broaden into bands.

If band width, W > this may not work ( low spin).

Stoner Model (Itinerant Magnets)

mSCF = 1.2 B

Band structure effects can lead

to high degeneracy near EF

magnetic instability and energy

lowering.

Stoner Criterion:

N(EF)I > 1

I ~ 0.7 – 0.9 eV for d elements.

Interaction Between Moments (Exchange)

• Moment formation by itself is not magnetism. Ordering is

required, and therefore interactions between moments on

different sites are what underlie magnetism.

• Some Mechanisms:

• Direct exchange – two atoms are touching (or very close) so

that their wavefunctions overlap. The interaction is like that

which gives rise to Hund’s first rule. It can be positive or

negative depending on the separation of the atoms, but it falls

off very strongly with distance.

• Super Exchange – coupling of spins through spin dependent

overlap typically involving other atoms.

• Conduction electron mediated exchange: e.g. RKKY,

magnetic semiconductors … Moments interact with

conduction electrons which mediate the coupling.

Conduction Electron Mediated Exchange

In weak interacting limit medium has some response, (q),

which defines the interaction through (ri-rj). More generally the

response may differ for strong interactions at short range but at

long distance would still take RKKY type form in a metal.

Super Exchange and Related

Consider two magnetic ions which interact via O and consider

parallel and anti-parallel alignments of the moments:

Parallel

Global Spin Direction

A

Maj. Min.

B

Maj. Min.

A

Maj. Min.

B

Maj. Min.

Anti-parallel

Band Formation In the absence of spin orbit and non-collinear structures hopping

is separate for spin up and spin down.

Parallel Case:

Global Spin Direction

A

Maj. Min.

B

Maj. Min.

Parallel Case with hopping:

A

Maj. Min. Maj. Min.

B

Band Formation In the absence of spin orbit and non-collinear structures hopping

is separate for spin up and spin down.

Global Spin Direction

Anti-parallel Case: Anti-parallel with hopping:

A

Maj. Min.

B

Maj. Min.

A

Maj. Min.

B

Maj. Min.

Antiferromagnetic Super Exchange

Global Spin Direction

Anti-parallel with hopping:

A

Maj. Min.

B

Maj. Min.

EF

Average energy of

occupied states is

lowered. Favors

antiferromagnetic

alignment (super

exchange)

Ferromagnetic Exchange

Global Spin Direction

EF

Average energy of

occupied states is

lowered. Favors

ferromagnetic

alignment (super

exchange).

This is the nature of

the double exchange

in manganites: It

competes with Jahn-

Teller, which would

split the eg level.

A

Maj. Min. Maj. Min.

B

What Favors Strong Super Exchange?

• In perovskites the interaction

proceeds through O.

1.High spin state.

2.Bond angles that favor M – O

– M hopping (i.e. 180o for eg).

3.Strong hybridization with O.

• Large orbitals that overlap

strongly with O (eg much

better than t2g).

• Short M-O neighbor

distances.

• d-states that are close in

energy to the O p states

(e.g. high metal valence

states like Cu2+).

Example: Cuprate Superconductors (Spin ½)

Tl2Ba2CuO6 Note hybridization of

Cu and in-plane O(1)

Highest Tc cuprates have long apical

O bond (and short in plane bonds),

are hole doped and have flat CuO2

planes (straight bonds).

An Example (R2NiMnO6) Double Perovskite

Azuma et al., Oratani et al., Mater et al., DJS et al.

A ferromagnet via standard Anderson super exchange.

Another Example PbVO3

Perovskite, polar tetragonal structure P4mm; extreme c/a ~ 1.23.

Shpanchenko (2004), Belik (2005), Uratani (2005), DJS (2006).

Ionic model: Pb2+V4+(O2-)3

• Two stereochemically active ions:

• Pb2+ on A-site

• V4+ on B-site (also magnetic)

• No transition with T up to 570K

• Tetragonal to Cubic transition at

P~2 GPa.

Pb

O

V

Perovskite Instabilities

•B-site driven:

• Classic ferroelectrics (e.g. BaTiO3)

• B-site – O hybridization is important.

•A-site driven:

• Tilted structures (e.g. CaTiO3)

• A-site stereochemical activity (Pb – O hybridization) can

give strong ferroelectricity (e.g. PZT).

• Morphotropic phase boundaries (piezoelectrics).

• Short FE coherence length interesting nanostructures

and high temperature relaxors.

•PbVO3 has strong stereochemical activity on both A-

and B-site positions. Super properties?

Hybridization Schemes PZT PbVO3

6s

6p

2p

3d/4d

EF

See Cohen (1992).

Pb O Zr/Ti Pb O V

c/a ~ 1.015 – 1.06, TC ~ 250 – 450 °C c/a ~ 1.23, TC unknown

6s

6p

2p

3d

?

V4+ in Oxides Two normal configurations:

CaVO3, SrVO3

Sr2VO4 ….

K2V3O8 ….

PbVO3

Metal or Mott Insulator. Magnetic insulator.

Short bond (1.55 – 1.60 Å)

Moment Formation in PbVO3

•LDA Calculations with LAPW method, c.f. Shpanchenko, Uratani.

•Stable local moments on V (ms=1B).

•Ground state is AF C-type.

Conf. E(meV)

NSP 0

F -111.2

G -127.3

A -91.8

C -127.8

The Vanadyl Bond

O p

V d t2g

eg

O p O p

z2

x2-y2

xy

xz,yz

O p

EF

Isotropic Octahedral Vanadyl Hund’s SrVO3, CaVO3 PbVO3

Structure of PbVO3

•LDA Structure Relaxation (FM PbVO3):

LDA Expt.

zV 0.5689 0.5668

zO1 0.2158 0.2102

zO2 0.6872 0.6889

(ag)=190, 408, 838 cm-1

V-O bond length = 1.67Å.

Why does PbVO3 form a highly tetragonal structure with short V-O

bond, while SrVO3 and CaVO3 do not?

Not ion size (c.f. Sr, Ca).

Metastable structure that could be made with e.g. CaVO3?

Structure of PbVO3

Does the V-O vanadyl bond form because of ionic forces?

LDA calculations for hypothetical CaVO3 in the PbVO3 structure.

PbVO3(FM) CaVO3(FM)

M(B) 1.0 0.88

FV(mRy/a0) 0* 80

Large force pushing

vanadyl bond apart

V moment is reduced

CaVO3 (FM)

PbVO3 structure Vanadyl destabilized.

t2g bands broadened.

V moment is reduced.

Reason is competition of V-O

and Pb-O hybridization in PbVO3.

MAGNETOELASTIC COUPLINGS

Why is Magnetism Coupled to the Lattice?

1. Moment formation affects bonding.

• Difference in size of high spin and low spin ions (Shannon).

• Moment formation competes with bonding (bonds have

paired electrons in normal cases) -- Invar

2. Exchange interactions depend on structure through hopping

integrals and on-site terms (relative shifts in levels).

3. Relativistic effects (spin orbit and Dzyaloshinsky-Moria) couple

spin directions to the lattice – magnetostriction, moment

canting.

How Does It Work?

Heisenberg Model J ~ t2/E

But both E and t depend on position – The hopping t is from

wave function overlap, which is very strongly dependent on

distance (exponential) and bond angles. J J(ri-rj,)

J J

J J

“Spin-Dimer”

A kind of bonding

Can accomplish the same thing with M – O – M bond angles in

perovskites or by lattice strain (e.g. MnO).

Big Effects Ibarra et al.,PRL (1995).

Large lattice signatures

of changes in magnetic

order with eg electrons.

SOMETHING NEW:

A-Site Disorder

ROTATIONAL MODE

• Distortion around A

(A-O bond lengths)

• Bends B-O-B bonds

but only bond

lengths in second

order. (n.b. breathing

mode is usually stiff).

• Driven by pressure

and/or tolerance

factor if octahedra

are stiff.

• Alternate is A-site

off-centering (Pb).

What If …

… we could eliminate the tilt instability from

arbitrary t<1 perovskites?

CdTiO3 and Alloys with PbTiO3

“Ferroelectric CdTiO3”

Density functional calculations for CdTiO3 (small tolerance factor,

possibly interesting chemistry)

• CdTiO3 has antiferroelectric ground

state.

• If forced ferroelectric it has a large

tetragonal strain in the tetragonal

FE state, and high energy scale.

• Supercells for 50-50 CdTiO3-

PbTiO3 are borderline ferroelectric

and tetragonal and have a large

c/a~1.08 (higher than PbTiO3).

S.V. Halilov, M. Fornari and D.J. Singh, Appl. Phys. Lett. 81, 3443 (2002).

Experimental Confirmation

This was the second example of an alloy with PbTiO3 that increases c/a.

Phonons In Ferroelectric Perovskites

First Principles Calculations

of Ghosez et al. (1999):

• note R point instabilities in

PZ and PT but not BT.

• Note different coherence

lengths for zone center

and zone boundary

instabilities.

ROTATIONAL MODE

Can we use disorder to

exploit the difference in

coherence length between

rotational and ferroelectric

instabilities?

Hypothetical Perovskite: K0.5Li0.5NbO3

• K and Li have very different sizes (1.8Å vs. 1.1Å).

• What if we make a perovskite alloying K and Li on the A-site?

• Strong off-centering of Li (A-site driven ferroelectric) – Tilt does not happen.

D.I. Bilc and D.J. Singh, PRL 96, 147602 (2006).

Single ion off-centering

•Reason for tetragonal state is the very large displacement of Li.

LATTICE INSTABILITIES IN PEROVSKITES

(Design Rules)

1. Hybridization between unoccupied A-site states and O 2p

states favors ferroelectricity in t<1 perovskites.

2. Alloying small A-site ions favor large tetragonality if

ferroelectricity can be obtained – e.g. CdTiO3 - PT

3. In materials with stiff octahedra, frustration due to a

mixture of large and small A-site ions, can stabilize

ferroelectricity due to the short coherence length of the

ferroelectric instability and the long rotational coherence

length.

4. The balance between tetragonal and rhombohedral ground

states (i.e. the MPB) can be controlled via the BO6 polarizability

– e.g. NbO6 vs. TaO6

Ba1-xCaxTiO3

1) Tc is maintained high under Ca alloying

even though the average tolerance factor

is strongly decreasing.

2) The system becomes much more

tetragonal as Ca is added.

A-Site Alloys with Bi

• Bi0.5Sr0.5Zn0.5Nb0.5O3 was reported in perovskite structure by

Kosyachenko et al. [Neorg. Mater. 18, 1352 (1982)] and

evidence pointing towards ferroelectricity was found.

• Bi0.5Pb0.5Zn0.5Nb0.5O3 would be the 50-50 solid solution of PZN

with hypothetical BiZn2/3Nb1/3O3.

• (Na,Bi)TiO3 is a known material that has been investigated alone

and in alloys with PbTiO3 and KNbO3.

• Bi(Zn0.5Ti0.5)O3 was shown to be a super tetragonal ferroelectric

with very high polarization by Suchomel and Davies [APL 86,

262905 (2005)].

(Bi,Pb)2ZnNbO6 Supercells

NaCl (111) layers

Pb

Bi

A-type (100) layers

C-type [001] chains Clusters

• Charge difference of Nb5+

and Zn2+ is 3 favors

chemical ordering.

• PbZn1/3Nb2/3O3 (PMN) has a

two sub-lattice (double

perovskite based) structure

should be stronger for

Zn:Nb ratio at 1:1.

• Done at LDA lattice

parameter somewhat

compressed [3.99 Å for Pb

and 3.97 Å for Sr]

• LDA calculations for 40-

atom double perovskite

supercells with various Bi/Pb

orderings and rocksalt Bi/Sr

ordering.

BiPbZnNbO6 Relaxed G-type cell at LDA lattice parameter (3.99 Å), pseudo-cubic

Cation off-centerings

in O cages

• Large off-centerings of Bi, but also

substantial for other ions, including Nb.

• Off-centering is along [111].

• Similar results for other three supercells.

S. Takagi, A. Subedi, D.J. Singh and V.R. Cooper, Phys. Rev. B 81, 134106 (2010)

BiPbZnNbO6 • G-type cell was relaxed as a function of tetragonal strain

• Minimum energy was at a c/a ratio of ~1.015, but this appears to be due to

tilts, not ferroelectricity (supercell artifact)

Off-centerings for

imposed c/a=1.0606

Note that off-

centering does not

switch to [001]

even with large

imposed strain.

BiPbZnNbO6

G-type supercell as a function of pseudo-cubic lattice parameter:

• Increasing off-centering with increasing volume, as usual (LDA

may underestimate).

• Substantial off-centerings of Nb.

Electronic Structure

• Note sizable band gap even at the

LDA level. Also note ions in

stable valence configurations for

oxides consistent with good

insulating behavior.

• Substantial hybridization of O 2p

states with Bi p, Pb p, Nb d.

Eg =2.7 eV (LDA)

Polarization: BiSrZnNbO6 and the Role of Pb

BiSrZnNbO6

• Known compound that readily forms in perovskite

structure.

• Average A-site charge is +2.5 Av. B-site is +3.5

(better for stability of perovskite).

• Polarization is comparable to pure Bi compounds

even though there is only 50% Bi.

• Reason is large Bi displacement & Nb off-centering.

BiSrZnNbO6 – Bi2ZnTiO6 Solid Solution

• Bi(Zn,Ti)O3 has a very large polarization ~150 µC/cm2 but is

essentially non-switchable due to super-tetragonality, c/a ~ 1.2

(Suchomel, 2006).

• Can we produce a useful MPB by alloying – key may be to alloy

with a strongly R material that produces an MPB far from the

BZT end so that it can be switchable.

• We did supercell calculations for the pseudo-binary solid

solution with BiSrZnNbO6.

• We used 40 and 80 atom cells with Zn and (Ti,Nb) on separate

sublattices (i.e. double perovskite).

BiSrZnNbO6 – Bi2ZnTiO6 Solid Solution

Average cation off-centerings in supercells:

Proposed Phase Diagram

Direction of P relative to 111 and 100:

• We find a region with a possible MPB and high polarization,

although the tetragonality on the T side is still very high.

Summary

The mineral

perovskite:

CaTiO3

“A minor ore of Ti”

… pretty interesting

physics though

Image from www.mindat.org: (mineral from Chelyabinsk, Russia)